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  • Draw a circuit with resistors in parallel and in series.
  • Calculate the voltage drop of a current across a resistor using Ohm’s law.
  • Contrast the way total resistance is calculated for resistors in series and in parallel.
  • Explain why total resistance of a parallel circuit is less than the smallest resistance of any of the resistors in that circuit.
  • Calculate total resistance of a circuit that contains a mixture of resistors connected in series and in parallel.

Most circuits have more than one component, called a resistor    that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance    . The simplest combinations of resistors are the series and parallel connections illustrated in [link] . The total resistance of a combination of resistors depends on both their individual values and how they are connected.

In part a of the figure, resistors labeled R sub 1, R sub 2, R sub 3, and R sub 4 are connected in series along one path of a circuit. In part b of the figure, the same resistors are connected along parallel paths of a circuit.
(a) A series connection of resistors. (b) A parallel connection of resistors.

Resistors in series

When are resistors in series    ? Resistors are in series whenever the flow of charge, called the current    , must flow through devices sequentially. For example, if current flows through a person holding a screwdriver and into the Earth, then R 1 size 12{R rSub { size 8{1} } } {} in [link] (a) could be the resistance of the screwdriver’s shaft, R 2 size 12{R rSub { size 8{2} } } {} the resistance of its handle, R 3 size 12{R rSub { size 8{3} } } {} the person’s body resistance, and R 4 size 12{R rSub { size 8{4} } } {} the resistance of her shoes.

[link] shows resistors in series connected to a voltage    source. It seems reasonable that the total resistance is the sum of the individual resistances, considering that the current has to pass through each resistor in sequence. (This fact would be an advantage to a person wishing to avoid an electrical shock, who could reduce the current by wearing high-resistance rubber-soled shoes. It could be a disadvantage if one of the resistances were a faulty high-resistance cord to an appliance that would reduce the operating current.)

Two electrical circuits are compared. The first one has three resistors, R sub one, R sub two, and R sub three, connected in series with a voltage source V to form a closed circuit. The first circuit is equivalent to the second circuit, which has a single resistor R sub s connected to a voltage source V. Both circuits carry a current I, which starts from the positive end of the voltage source and moves in a clockwise direction around the circuit.
Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right).

To verify that resistances in series do indeed add, let us consider the loss of electrical power, called a voltage drop    , in each resistor in [link] .

According to Ohm’s law    , the voltage drop, V size 12{V} {} , across a resistor when a current flows through it is calculated using the equation V = IR size 12{V= ital "IR"} {} , where I size 12{I} {} equals the current in amps (A) and R size 12{R} {} is the resistance in ohms Ω size 12{ left ( %OMEGA right )} {} . Another way to think of this is that V size 12{V} {} is the voltage necessary to make a current I size 12{I} {} flow through a resistance R size 12{R} {} .

So the voltage drop across R 1 size 12{R rSub { size 8{1} } } {} is V 1 = IR 1 size 12{V rSub { size 8{1} } = ital "IR" rSub { size 8{1} } } {} , that across R 2 size 12{R rSub { size 8{2} } } {} is V 2 = IR 2 size 12{V rSub { size 8{2} } = ital "IR" rSub { size 8{2} } } {} , and that across R 3 size 12{R rSub { size 8{3} } } {} is V 3 = IR 3 size 12{V rSub { size 8{3} } = ital "IR" rSub { size 8{3} } } {} . The sum of these voltages equals the voltage output of the source; that is,

V = V 1 + V 2 + V 3 . size 12{V=V rSub { size 8{1} } +V rSub { size 8{2} } +V rSub { size 8{3} } } {}

This equation is based on the conservation of energy and conservation of charge. Electrical potential energy can be described by the equation PE = qV size 12{ ital "PE"= ital "qV"} {} , where q size 12{q} {} is the electric charge and V size 12{V} {} is the voltage. Thus the energy supplied by the source is qV size 12{ ital "qV"} {} , while that dissipated by the resistors is

qV 1 + qV 2 + qV 3 . size 12{ ital "qV" rSub { size 8{1} } + ital "qV" rSub { size 8{2} } + ital "qV" rSub { size 8{3} } } {}

Connections: conservation laws

The derivations of the expressions for series and parallel resistance are based on the laws of conservation of energy and conservation of charge, which state that total charge and total energy are constant in any process. These two laws are directly involved in all electrical phenomena and will be invoked repeatedly to explain both specific effects and the general behavior of electricity.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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Can you compute that for me. Ty
Jude
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emma Reply
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what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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Magreth
progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
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Source:  OpenStax, Introductory physics - for kpu phys 1100 (2015 edition). OpenStax CNX. May 30, 2015 Download for free at http://legacy.cnx.org/content/col11588/1.13
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